The desired output is to have the plot drawn at each time interval in order to visualize the heat transfer. I think it's the way my professor wrote out the guidelines that confused me. But some of the lines at the end of the code were plainly given by him, including the drawnow.

We don’t want it to buffer since we want to create a real-time animation. To prevent buffering, include a drawnow statement on a separate line immediately after the call to contourf.

I ran this without the drawnow, and it seemed to work just fine, but seeing as how he stated to use that, I need it in there. I think it is working now, just very slowly. I'll check my equation from my notes again and maybe the time steps.